Fraternitè
On July 14, 1789, all brothers in a family calculated the sum of their ages and then the sum of their years of birth. It turned out that . How many of them were born in March at most?
The answer is 1.
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1 solution
a is referred to the number of brothers born by 14 July and b the number of those born after. It is 1 7 8 8 1 = a 1 7 8 9 + b 1 7 8 8 = ( a + b ) 1 7 8 8 + a . Since 1 7 8 8 1 < 1 7 8 8 2 we get ( a + b ) < 1 7 8 8 . So (a + b) is the quotient 10 of the division of 17881 for 1788 and b is the rest 1. Thus there is 10 brothers, of which 9 born after July 14 and at most one may be born in March.